Sharp Quantitative Stability for the Affine \(p\)-Sobolev Inequality, Part I: The Case \(2≤ p<n\)

2026/06/08 by Song Fan, Gui-Dong Li, Jianjun Zhang
#math.AP

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Abstract

We prove a sharp quantitative stability result for the affine \(L^p\)-Sobolev inequality, for \(p≥2\), introduced by Lutwak--Yang--Zhang (J. Differential Geom., 62 (2002), 17--38). Moreover, the stability exponent is shown to be optimal, and equal to \(p\).

Citations

• Sharp Stability for the Affine Fractional Sobolev Inequality

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• Sharp Stability for the Affine Fractional Sobolev Inequality

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